I could be wrong, but I suspect it's because the HDs do not have Flash installed on them (thanks to Adobe discontinuing Flash support for mobile devices). Try installing the Puffin browser from the B&N app store and opening Youtube through it. Doing that might work.

But to the OP's problem Youtube should play fine out of the box. Youtube is optimized for mobile devices and doesn't use Flash. So if it is not working something isn't right with the tablet, settings, browser settings, or similar. I'd figure that out before I find a workaround.

I have had a similar problem on one of our Nook HD+'s. We bought one in March and with the exception of having to unregister and reregister it once after the GooglePlay store became available, we've had few problems.

We bought a second one lst month for our oldest, and it first it worked fine. About a week ago we started getting the "Unfortunately, Youtube has stopped" message when launched from the app. Using the Chrome browser, it just won't load. This only happens on the children's profile. If I switch it to my profile, youtube works fine. This does not happen on our other Nook HD+.

Yesterday, I called tech support. After about 1 1/2 hours of them trying to get it to work, they decided that it must be a software error and are sending us a new Nook HD+. I am glad for their willingness to do that, but I don't exactly have confidence that it will fix the problem.